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cyqdesign 2016-06-21 11:24

Speckle Phenomena in Optics: Theory and Applications

Speckle Phenomena in Optics: Theory and Applications !\#Wq{p>W*  
G/JGb2I/7|  
Joseph W. Goodman ^$'{:i  
5ih>x3S1/  
Contents b"$?(Y  
1 Origins and Manifestations of Speckle 1 (wL$ h5SG  
1.1 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8Ay7I  
1.2 Intuitive Explanation of the Cause of Speckle . . . . . . . . . . . . . . . . . . . . . . . . . 2 d*tWFr|J-  
1.3 Some Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 )<HvIr(xr  
2 Random Phasor Sums 7 `!cdxKLR  
2.1 First and Second Moments of the Real and Imaginary Parts of the Resultant Phasor . . . . . 8 hr]+ 4!/  
2.2 Random Walk with a Large Number of Independent Steps . . . . . . . . . . . . . . . . . . 9 IN/$b^Um  
2.3 Random Phasor Sum Plus a Known Phasor . . . . . . . . . . . . . . . . . . . . . . . . . . 12 V<5. 4{[G  
2.4 Sums of Random Phasor Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3u j|jwL  
2.5 Random Phasor Sums with a Finite Number of Equal-Length Components . . . . . . . . . 16 Osz=OO{  
2.6 Random Phasor Sums with a Nonuniform Distribution of Phases . . . . . . . . . . . . . . . 17 'TYO-'aC  
3 First-Order Statistical Properties of Optical Speckle 23 ';G/,wB?`  
3.1 Definition of Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 /}1|'?P  
3.2 First-Order Statistics of the Intensity and Phase . . . . . . . . . . . . . . . . . . . . . . . . 24 B!mHO*g  
3.2.1 Large Number of Random Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 mo<*h&;&  
3.2.2 Constant Phasor plus a Random Phasor Sum . . . . . . . . . . . . . . . . . . . . . 27 |"K%Tvxe  
3.2.3 Finite Number of Equal-Length Phasors . . . . . . . . . . . . . . . . . . . . . . . . 31 oU )(/  
3.3 Sums of Speckle Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y[e.1\d'  
3.3.1 Sums on an Amplitude Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 _1?uAQ3,  
3.3.2 Sum of Two Independent Speckle Intensities . . . . . . . . . . . . . . . . . . . . . 34 WzFXF{(  
3.3.3 Sum of N Independent Speckle Intensities . . . . . . . . . . . . . . . . . . . . . . 37 f&$Bjq  
3.3.4 Sums of Correlated Speckle Intensities . . . . . . . . . . . . . . . . . . . . . . . . 40 <%.%q  
3.4 Partially Polarized Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2 K_ QZ  
3.5 Partially Developed Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 >h%>s4W  
3.6 Speckled Speckle, or Compound Speckle Statistics . . . . . . . . . . . . . . . . . . . . . . 47 /\Nc6Z/ L  
3.6.1 Speckle Driven by a Negative Exponential Intensity Distribution . . . . . . . . . . . 48 Xc NL\fl1  
3.6.2 Speckle Driven by a Gamma Intensity Distribution . . . . . . . . . . . . . . . . . . 50 g5#LoGc  
3.6.3 Sums of Independent Speckle Patterns Driven by a Gamma Intensity Distribution . . 51 J t.<Z&  
4 Higher-Order Statistical Properties of Optical Speckle 55 7[=G;2<  
4.1 Multivariate Gaussian Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 _v#pu Fy  
4.2 Application to Speckle Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 @"s<0T^H  
4.3 Multidimensional Statistics of Speckle Amplitude, Phase and Intensity . . . . . . . . . . . . 58 (P? |Bk [  
4.3.1 Joint Density Function of the Amplitudes . . . . . . . . . . . . . . . . . . . . . . . 59 S8qg"YR  
4.3.2 Joint Density Function of the Phases . . . . . . . . . . . . . . . . . . . . . . . . . . 60 ~ ?nn(Q-  
4.3.3 Joint Density Function of the Intensities . . . . . . . . . . . . . . . . . . . . . . . . 64 A'CD,R+gR  
4.4 Autocorrelation Function and Power Spectrum of Speckle . . . . . . . . . . . . . . . . . . . 66 ]a.e;c-  
4.4.1 Free-Space Propagation Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 J jZB!Lg=  
4.4.2 Imaging Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Z5'^Hj1,  
4.4.3 Speckle Size in Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 .pZYPKMaE  
4.5 Dependence of Speckle on Scatterer Microstructure . . . . . . . . . . . . . . . . . . . . . . 77 ;S^"Y:7)  
4.5.1 Surface vs. Volume Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 D0 k ,8|  
4.5.2 Effect of a Finite Correlation Area of the ScatteredWave . . . . . . . . . . . . . . . 78 bCP2_h3*  
4.5.3 A Regime where Speckle Size Is Independent of Scattering Spot Size . . . . . . . . 81 f'ld6jt|%  
4.5.4 Relation between the Correlation Areas of the ScatteredWave and the Surface Height .feB VRg  
Fluctuations— Surface Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 83 zU[o_[+7^  
4.5.5 Dependence of Speckle Contrast on Surface Roughness— Surface Scattering . . . . 88 Wj3i*x$  
4.5.6 Properties of Speckle Resulting from Volume Scattering . . . . . . . . . . . . . . . 92 QN;5+p[N  
4.6 Statistics of Integrated and Blurred Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . 94 x]YzVJ=Y  
4.6.1 Mean and Variance of Integrated Speckle . . . . . . . . . . . . . . . . . . . . . . . 95 W0x9^'=s\  
4.6.2 Approximate Result for the Probability Density Function of /*gs]  
Integrated Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3VU4E|s>  
4.6.3 “Exact” Result for the Probability Density Function of Integrated Intensity . . . . . 101 Ma\%uEgTD  
4.6.4 Integration of Partially Polarized Speckle Patterns . . . . . . . . . . . . . . . . . . . 106 q;R&valn  
4.7 Statistics of Derivatives of Speckle Intensity and Phase . . . . . . . . . . . . . . . . . . . . 108 w)J-e gc  
4.7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 "E7<S5 cr  
4.7.2 Parameters for Various Scattering Spot Shapes . . . . . . . . . . . . . . . . . . . . 110 V %[t'uh  
4.7.3 Derivatives of Speckle Phase: Ray Directions in a Speckle Pattern . . . . . . . . . . 111 M%54FsV  
4.7.4 Derivatives of Speckle Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 (soTkH:#  
4.7.5 Level Crossings of Speckle Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . 116 ~c&sr5E  
4.8 Zeros of Speckle Patterns: Optical Vortices . . . . . . . . . . . . . . . . . . . . . . . . . . 118 r[):'ys,C  
4.8.1 Conditions Required for a Zero of Intensity to Occur . . . . . . . . . . . . . . . . . 119 :)Es]wA#HZ  
4.8.2 Properties of Speckle Phase in the Vicinity of a Zero of Intensity . . . . . . . . . . . 119 \$Ky AWrZi  
4.8.3 The Density of Vortices in Fully Developed Speckle . . . . . . . . . . . . . . . . . 119 X)(K|[  
4.8.4 The Density of Vortices for Fully Developed Speckle Plus a Coherent Background . 123 >l-u{([B  
5 OpticalMethods for Suppressing Speckle 125 ~9rNP{+  
5.1 Polarization Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 s8:epcL`A  
5.2 Temporal Averaging with a Moving Diffuser . . . . . . . . . . . . . . . . . . . . . . . . . 127 cl#XiyK>  
5.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 `[E-V  
5.2.2 Smooth Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 x xzUey  
5.2.3 Rough Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 $C=XSuPNK  
5.3 Wavelength and Angle Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 CUdpT$$x3  
5.3.1 Free-Space Propagation, Reflection Geometry . . . . . . . . . . . . . . . . . . . . 136 MZ0cZv$v!~  
5.3.2 Free-Space Propagation, Transmission Geometry . . . . . . . . . . . . . . . . . . . 144 1LFad>`  
5.3.3 Imaging Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 BbFLT@W4  
5.4 Temporal and Spatial Coherence Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 150 IW@xT@  
5.4.1 Coherence Concepts in Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 x_8sV?F  
5.4.2 Moving Diffusers and Coherence Reduction . . . . . . . . . . . . . . . . . . . . . . 152 l %zbx"%x  
5.4.3 Speckle Suppression by Reduction of Temporal Coherence . . . . . . . . . . . . . . 154 <%^WZ:c  
5.4.4 Speckle Suppression by Reduction of Spatial Coherence . . . . . . . . . . . . . . . 157 |,KsJ2hD  
5.5 Use of Temporal Coherence to Destroy Spatial Coherence . . . . . . . . . . . . . . . . . . 163 oFyB-vpYQV  
5.6 Compounding Speckle Suppression Techniques . . . . . . . . . . . . . . . . . . . . . . . . 163 w&#[g9G%  
6 Speckle in Certain Imaging Modalities 165 KBi(Ns#+  
6.1 Speckle in the Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Q7`)&^ Hx  
6.2 Speckle in Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6f0o'  
6.2.1 Principles of Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 i.K!;E>  
6.2.2 Speckle Suppression in Holographic Images . . . . . . . . . . . . . . . . . . . . . . 170 L\#G#1x8  
6.3 Speckle in Optical Coherence Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . 171 l' Li!u  
6.3.1 Overview of the OCT Imaging Technique . . . . . . . . . . . . . . . . . . . . . . . 172 kDJqT  
6.3.2 Analysis of OCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 NH5sV.vvc  
6.3.3 Speckle and Speckle Suppression in OCT . . . . . . . . . . . . . . . . . . . . . . . 176 .|DrXJ \c  
6.4 Speckle in Optical Projection Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 2 N(Z^  
6.4.1 Anatomies of Projection Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 $uwz` N:  
6.4.2 Speckle Suppression in Projection Displays . . . . . . . . . . . . . . . . . . . . . . 182 #v$wjqK5  
6.4.3 Polarization Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 RI<s mt.Ng  
6.4.4 A Moving Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 sJQ~ :p0e  
6.4.5 Wavelength Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 H #X*OJ  
6.4.6 Angle Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 _lT'nFe =Q  
6.4.7 Over-Design of the Projection Optics . . . . . . . . . . . . . . . . . . . . . . . . . 186 L B.B w  
6.4.8 Changing Diffuser Projected onto the Screen . . . . . . . . . . . . . . . . . . . . . 188 O.Te"=^"F  
6.4.9 Specially Designed Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 g"!cO^GkT  
6.5 Speckle in Projection Microlithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 P1L+Vnfu  
6.5.1 Coherence Properties of Excimer Lasers . . . . . . . . . . . . . . . . . . . . . . . 200 S,|ZCl>+  
6.5.2 Temporal Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 "7fEL:|j  
6.5.3 From Exposure Fluctuations to Line Position Fluctuations . . . . . . . . . . . . . . 202 K)1Lg? j  
7 Speckle in Certain Non-imagingModalities 205 ' 8R5 Tl  
7.1 Speckle in Multimode Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 o3GZcH?  
7.1.1 Modal Noise in Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 ?&qQOM~b-\  
7.1.2 Statistics of Constrained Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 fhdqes])  
7.1.3 Frequency Dependence of Modal Noise . . . . . . . . . . . . . . . . . . . . . . . . 211 >'m&/&h  
7.2 Effects of Speckle on Optical Radar Performance . . . . . . . . . . . . . . . . . . . . . . . 216 S^i8VYK,C5  
7.2.1 Spatial Correlation of the Speckle Returned from Distant Targets . . . . . . . . . . . 217 ETX>wZ  
7.2.2 Speckle at Low Light Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 li{<F{7  
7.2.3 Detection Statistics—Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . 222 7F2:'3SQ  
7.2.4 Detection Statistics— Heterodyne Detection . . . . . . . . . . . . . . . . . . . . . 227 5Uhxl^c  
7.2.5 Comparison of Direct Detection and Heterodyne Detection . . . . . . . . . . . . . . 234 iBWEZw)  
7.2.6 Reduction of the Effects of Speckle in Optical Radar Detection . . . . . . . . . . . . 235 ]4')H;'y  
7.3 Speckle and Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 $t6t 6<M)  
8 Speckle in Imaging Through the Atmosphere 239 SMd[*9l [  
8.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 WcXNc`x  
8.1.1 Refractive Index Fluctuations in the Atmosphere . . . . . . . . . . . . . . . . . . . 239 _h,X3P   
8.2 Short-Exposure and Long-Exposure Point-Spread Functions . . . . . . . . . . . . . . . . . 240 [(3 %$?[  
8.3 Long-Exposure and Short-Exposure Average Optical Transfer Functions . . . . . . . . . . . 242 gDw(_KC  
8.4 Statistical Properties of the Short-Exposure OTF and MTF . . . . . . . . . . . . . . . . . . 243 j)nE!GKD(  
8.5 Astronomical Speckle Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 4QPHT#eqX  
8.5.1 Object Information that Is Retrievable . . . . . . . . . . . . . . . . . . . . . . . . . 248 ] fA5D)/m<  
8.5.2 Results of a More Complete Analysis of the Form of the Speckle Transfer Function . 250 kE+fdr\ T  
8.6 The Cross-Spectrum or Knox–Thompson Technique . . . . . . . . . . . . . . . . . . . . . 252 ~rq:I<5  
8.6.1 The Cross-Spectrum Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . 253 BTO l`U  
8.6.2 Recovering Full Object Information from the Cross-Spectrum . . . . . . . . . . . . 254 J?E!\V&U  
8.7 The Bispectrum Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 fS8Pi,!  
8.7.1 The Bispectrum Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 2h}FotlO  
8.7.2 Recovering Full Object Information from the Bispectrum . . . . . . . . . . . . . . . 258 q)@;8Z=_c  
8.8 Speckle Correlography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 EronNtu8i  
A Linear Transformations 263 ^[+2P?^K  
B Contrast of Partially Developed Speckle 267 %k"hzjXAw  
C Statistics of Derivatives of Speckle 271 bz,"TG[  
C.1 The Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 KB^GC5L>  
C.2 Joint Density Function of the Derivatives of Phase . . . . . . . . . . . . . . . . . . . . . . . 274 7)>L#(N  
C.3 Joint Density Function of the Derivatives of Intensity . . . . . . . . . . . . . . . . . . . . . 274 gC%$)4-:  
D Wavelength and Angle Dependence 277 P3a]*>.,  
D.1 Free-Space Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 U3M;{_g  
D.2 Imaging Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 z0YL,  
E Speckle Contrast when a Dynamic Diffuser is Projected onto a Random Screen 285 JHg;2xm"<K  
E.1 Random Phase Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6Y.k<oem  
E.2 Diffuser that Just Fills the Projection Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 287 ojJu a c4  
E.3 Diffuser Overfills the Projection Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 OB+cE4$  
F Statistics of Constrained Speckle 289 ^4[QX -_2  
Bibliography 291 g<w1d{Td  
Index 299
measure123 2016-06-21 11:26
感谢分享，好书
mang2004 2016-06-25 10:51
经典，谢谢。
herrok 2016-06-25 23:16
谢谢楼主！
mumapiaoyun 2016-07-05 21:29
好高深，了解学习下
光强 2016-07-06 23:32
Speckle Phenomena
东西南北 2016-09-17 20:59
学习来了  谢谢
alvin1989 2016-11-24 02:38
好书啊， 最近在做multimodefiber的实验，觉得这本书有一定作用  还有最近很火的利用speckle noise来做focusing
bairuizheng 2016-11-24 03:03
谢谢。 y#O/Xw  
hesi 2017-03-18 17:30
很清楚，谢谢！
bincao 2017-07-28 15:36
好书，谢谢
bmw0501 2017-08-02 09:58
好东西，谢谢 %yR 80mn8  
starnoy 2017-08-30 10:05
不错，好东西啊
sniper_2008 2018-07-18 19:08
谢谢分享资料！
老潘66 2018-12-16 21:37
谢谢分享。
老潘66 2018-12-16 21:37
谢谢，感谢
老潘66 2018-12-16 21:38
谢谢，楼主
老潘66 2018-12-16 21:38
内容可以。
hesi 2018-12-30 11:44
谢谢楼主！现在能找到的英文电子版跟最终出版的的好像都差第八章。英文电子版的第八章在出版时是第九章，参见中译本
tebsix 2018-12-30 15:12
好高深，了解学习下
k0184990 2019-02-20 01:54
感谢分享，好书
cgl155410 2019-02-20 08:55
感谢分享，好书
icecool258 2019-03-18 12:36
学习学习
arq2008 2021-12-01 17:56
谢谢楼主！
kendall 2022-04-03 09:24
优秀book，支持
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